Related papers: Equivariant Hamiltonian Flows
First we give an introduction to the method of diagonalizing or block-diagonalizing continuously a Hamiltonian and explain how this procedure can be used to analyze the two-dimensional Hubbard model. Then we give a short survey on…
Motivated by the viewpoint of integrable systems, we study commuting flows of 2-component quasilinear equations, reducing to investigate the solutions of the wave equation with non-constant speed. In this paper, we apply the reduction…
We present a framework for learning probability distributions on topologically non-trivial manifolds, utilizing normalizing flows. Current methods focus on manifolds that are homeomorphic to Euclidean space, enforce strong structural priors…
Self-supervised representation learning is able to learn semantically meaningful features; however, much of its recent success relies on multiple crops of an image with very few objects. Instead of learning view-invariant representation…
This work develops a symplectic framework for quantum computing to be applied to classical Hamiltonian systems, exploiting the intrinsic geometric compatibility between unitary quantum evolution and symplectic phase-space dynamics in a…
The Hamiltonian formulation of superfluids based on noncanonical Poisson brackets is studied in detail. The assumption that the momentum density is proportional to the flow of the conserved energy is shown to lead to the covariant…
Using the message-passing mechanism in machine learning (ML) instead of self-consistent iterations to directly build the mapping from structures to electronic Hamiltonian matrices will greatly improve the efficiency of density functional…
We propose a general framework to extend Flow Matching to homogeneous spaces, i.e. quotients of Lie groups. Our approach reformulates the problem as a flow matching task on the underlying Lie group by lifting the data distributions. This…
Hamiltonian Learning is a process of recovering system Hamiltonian from measurements, which is a fundamental problem in quantum information processing. In this study, we investigate the problem of learning the symmetric Hamiltonian from its…
Quantum process characterization is a fundamental task in quantum information processing, yet conventional methods, such as quantum process tomography, require prohibitive resources and lack scalability. Here, we introduce an efficient…
Given a collection of images, humans are able to discover landmarks by modeling the shared geometric structure across instances. This idea of geometric equivariance has been widely used for the unsupervised discovery of object landmark…
This study focuses on the novel application of a normalizing flow as a method of domain adaptation. Normalizing flows offer a way to transform data points between two different distributions. The present study investigates a method of…
Modeling complex systems that evolve toward equilibrium distributions is important in various physical applications, including molecular dynamics and robotic control. These systems often follow the stochastic gradient descent of an…
Normalizing flows are powerful non-parametric statistical models that function as a hybrid between density estimators and generative models. Current learning algorithms for normalizing flows assume that data points are sampled…
Lie symmetry group method is applied to study Newtonian incompressible fluid's equations flow in turbulent boundary layers. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are…
For a given differentiable map $(x,y)\to (X(x,y),Y(x,y))$, which has an inverse, we show that there exists a Hamiltonian flow in which x plays the role of the time variable while y is fixed.
Normalizing flows are invertible neural networks with tractable change-of-volume terms, which allow optimization of their parameters to be efficiently performed via maximum likelihood. However, data of interest are typically assumed to live…
Based on the manifold hypothesis, real-world data often lie on a low-dimensional manifold, while normalizing flows as a likelihood-based generative model are incapable of finding this manifold due to their structural constraints. So, one…
The marginal likelihood, or Bayesian evidence, is a crucial quantity for Bayesian model comparison but its computation can be challenging for complex models, even in parameters space of moderate dimension. The learned harmonic mean…
We establish kinetic Hamiltonian flows in density space embedded with the $L^2$-Wasserstein metric tensor. We derive the Euler-Lagrange equation in density space, which introduces the associated Hamiltonian flows. We demonstrate that many…